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Keywords:
presentation; order-decreasing mapping; order-preserving mapping; transformation semigroups
presentation; order-decreasing mapping; order-preserving mapping; transformation semigroups
Summary:
Let $[n]=\{1,\ldots ,n\}$ be an $n$-chain. We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-decreasing mappings of $[n]$, the semigroup of full order-preserving and order-decreasing mappings of $[n]$, the semigroup of partial one-to-one order-preserving and order-decreasing mappings of $[n]$, and the semigroup of partial order-preserving and order-decreasing mappings of $[n]$.
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